Remark 1.3 The analysis of growth estimates for eigenfunctions of the Laplacian and of other elliptic differential operators is still a problem of wide interest. In particular for its relation with the geometric analysis of nodal sets. For classic references on the subject we refer the reader to Sunada [1]}, Atiyah, Donnelly and Singer [2]}, Borel and Garland [3]}, Jerison and Lebeau [4]}, Donnelly and Fefferman [5]}, [6]}, [7]}, [8]}, Donnelly and Garofalo [9]}, [10]}, and Lin [11]}. As for recent works on the subject we refer the reader to Apraiz, Escauriaza, Wang, and Zhang [12]}, Blair and Sogge [13]}, Cavalletti and Farinelli [14]}, Enciso and Peralta-Salas [15]}, Georgiev [16]}, Kenig, Zhu, and Zhuge [17]}, Logunov [18]}, [19]}, Logunov, Malinnikova, Nadirashvili, and Nazarov [20]}, Tian and Yang [21]} and Toth and Zelditch [22]} just to mention a few. About the applications of spectral inequalities to the control theory we refer to Benabdallah and Naso [23]}, Fu, Lü, and Zhang [24]}, Lebeau and Robbiano [25]}, Lebeau and Zuazua [26]}, J.-L. Lions, [27]}, Micu and Zuazua [28]}, Miller [29]}, [30]}, Rousseau and Lebeau [31]}, Cardona [32]}, Rousseau and Robbiano [33]}, and the extensive list of references therein.

